Question

describe the possible lengths of the third side of the triangle if the lengths of the other two sides are 4 inches and 8 inches. \\( \square \\) in. \\( < x < \square \\) in.

Explanation:

Step1: Apply triangle inequality theorem

The triangle inequality theorem states that for a triangle with side lengths \(a\), \(b\), and \(c\), \(|a - b|\lt c\lt a + b\). Let \(a = 4\) and \(b=8\).

Step2: Calculate the lower - bound

\(|4 - 8|=| - 4| = 4\)

Step3: Calculate the upper - bound

\(4+8 = 12\)

Answer:

\(4\lt x\lt12\)